Scientific Method —

Drawing the line between liquid and gas

A combination of two existing methods results in a novel way to describe and …

While thermodynamics has long concerned itself with understanding the equilibrium between various phases, classical thermodynamics only cares about long-term behaviors that occur after equilibrium is reached. Modern approaches have started to answer questions about the dynamics of two phases and their interface. One of the earliest methods for directly simulating coexistence between two phases was the Gibbs Ensemble simulation, which allows researchers to directly compute the phase equilibrium behavior of two fluid phases. Unfortunately, it does so by completely ignoring the interface between them.

In order to model the actual interface of a liquid-gas equilibrium, one must use more complex simulation methodologies. Even with more complex methods, ones that give a highly detailed image of what is happening between the liquid and the gas, identifying the molecules that are at the interface itself is still a huge challenge. A paper that will appear in an upcoming issue of Physical Review E merges the fields of molecular simulation and computational geometry to create a novel method for identifying the molecules that are part of the interface.

The authors carried out molecular dynamics simulations of a population of about 2.5k molecules of Lennardjonesium (particles that are described by a Lennard-Jones potential) in order to model a liquid-gas equilibrium among the particles. After allowing the simulations an initial equilibration period, they were able to sample 5000 configurations in order to study the interface in detail.

To describe the interface, the authors used what is known as an ?-shape concept. Prior efforts have used Voronoi tessellations and Delaunay triangulations, both of which can help categorize, or provide a picture of, the structure of a disordered material. The idea behind an ?-shape is that it allows one to describe the shape of a given set of points or provide a clear definition of any border that appears between two surfaces. The ?-shape method is not as well defined as the two other methods, as different values of ? can result in vastly different surfaces.

To find the optimal value of ? in the ?-shape definition of a liquid-gas interface, the researchers compared the results produced by method to those derived using other, more complete, methods. They found that their method, when provided an optimal value for ?, is good, but not as good as the more complete minimum area method. However, their method is far less computationally expense than the minimum area method, almost a factor of ten faster at producing a solution.

This paper combines two previously known methods, but does so in a way that gives some insight into a phenomenon that is growing in importance in various fields. While the ?-shape model does not give us a complete answer, it is a great engineering solution—it gives us 90 percent of the answer in 10 percent of the time. If the quick-and-dirty method suggests that something looks promising, someone can then devote more time to performing an in-depth analysis of these cases.

Physical Review E, 2009. DOI: Upcoming

Matt Ford
Matt is a contributing writer at Ars Technica, focusing on physics, astronomy, chemistry, mathematics, and engineering. When he's not writing, he works on realtime models of large-scale engineering systems. Emailzeotherm@gmail.com//Twitter@zeotherm